Background

This document has nls (non-linear least squares) regression fits using the LOG-NORMAL functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass vs. stand age relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.

We considered the following Log-Normal functional form \(B = (1 + (yr-1990)* ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge_{t2} /c \right)} {d} \right]} ^2 \right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(STDAGE_{t2}\) is the stand age at the second of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot biomass interval, which is defined as the measurement time minus 10 years and a 30-year climate normal from 1960-1989, and \(yr\) is the measurement year (all FIA data). Free parameters are \(ge\): biomass growth enhancement over time, \(\alpha\): the growth compensation of lost plot biomass, \(a\): the y-intercept of the curve, \(a +b\): the peak value of \(B\), \(c\): the \(StdAge\) value at peak \(B\), and \(d\): the log-normal curve shape parameter.

Model selection is used to determine the best fitting models including \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or the difference in the Palmer drought severity index from June - August for the 10 years preceding the biomass measurement and the 1960-1989 period) and \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest).

model 1: simple model \(B = (1 + (yr-1990)* ge/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge_{t2} /c \right)} {d} \right]} ^2 \right)\)

model 2: phi model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge_{t2} /c \right)} {d} \right]} ^2 \right)\)

model 3: phi-alpha model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge_{t2} /c \right)} {d} \right]} ^2 \right)\)

Note:

This analysis only uses plot biomass data from the same plot locations and measurement intervals for which we also have data on biomass growth (which is used in the growth vs. biomass analysis ). We use the second of the two plot measurements comprising a \(G\) interval

This includes the following plot-based filtering criteria (which were used for the growth vs. biomass analysis):

  1. exclude FIA plots in plantation forests
  2. exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
  3. exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
  4. exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
  5. exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
  6. exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Error in eval(extras, data, env) : object 'P_211' not found
## Error in eval(extras, data, env) : object 'P_211' not found
## Error in as.formula(formula) : object 'f_ln_3' not found
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_211$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_211.", Mod.Sel1, sep = "")) : 
##   object 'nls_211.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

212 - Laurentian Mixed Forest

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1  18747     6234.1                          
## 2  18742     6234.1  5 0.04459  0.0268 0.9997
##   model      AIC
## 1     1 195208.2
## 2     2 195169.6
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  3.236e-01  1.122e-01   2.883  0.00395 ** 
## phi 0.000e+00  3.737e-03   0.000  1.00000    
## a   1.455e+01  5.817e-01  25.018  < 2e-16 ***
## b   8.846e+01  2.713e+00  32.608  < 2e-16 ***
## c   1.392e+02  6.409e+00  21.728  < 2e-16 ***
## d   1.545e+00  4.149e-02  37.235  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5767 on 18742 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1   7164       1238                              
## 2   7163       1238  1 -8.6288e-10       0      1
##   model      AIC
## 1     1 78202.93
## 2     2 78204.93
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   0.08165    0.11857   0.689    0.491    
## a   20.39460    2.05062   9.946   <2e-16 ***
## b  181.88353   10.48899  17.340   <2e-16 ***
## c  170.40292   17.10107   9.964   <2e-16 ***
## d    1.53641    0.08127  18.904   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4157 on 7164 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   4868     1470.5                          
## 2   4867     1469.8  1 0.69844  2.3127 0.1284
##   model      AIC
## 1     1 52441.03
## 2     2 52440.72
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge   -0.053033   0.214469  -0.247    0.805    
## phi   0.014505   0.009861   1.471    0.141    
## a    18.601955   1.752549  10.614   <2e-16 ***
## b   122.927550   7.357023  16.709   <2e-16 ***
## c   129.208530  10.051594  12.855   <2e-16 ***
## d     1.259903   0.070683  17.825   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5495 on 4867 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (4 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95381, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -30.683, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df     Sum Sq F value Pr(>F)
## 1   8771     1614.1                             
## 2   8770     1614.1  1 1.3285e-09       0 0.9999
##   model      AIC
## 1     1 92044.88
## 2     2 92046.88
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.22069    0.09077  -2.431   0.0151 *  
## a   25.73594    2.21843  11.601   <2e-16 ***
## b  112.88900    4.17602  27.033   <2e-16 ***
## c  113.57021    6.06064  18.739   <2e-16 ***
## d    1.36021    0.06503  20.918   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.429 on 8771 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df     Sum Sq F value Pr(>F)
## 1  12326     3355.8                             
## 2  12325     3355.8  1 8.5038e-11       0      1
##   model      AIC
## 1     1 133924.2
## 2     2 133926.2
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   0.87389    0.11956   7.310 2.85e-13 ***
## a   12.07604    0.64620  18.688  < 2e-16 ***
## b  146.74272    6.48658  22.622  < 2e-16 ***
## c  169.36771   16.98088   9.974  < 2e-16 ***
## d    1.99609    0.06812  29.303  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5218 on 12326 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (16 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1  12425     5068.8                              
## 2  12424     5065.8  1 3.0036  7.3664 0.006655 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 137933.1
## 2     2 137927.8
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  5.754e-01  1.346e-01   4.275 1.92e-05 ***
## phi 1.604e-02  5.891e-03   2.723  0.00648 ** 
## a   1.168e+01  7.745e-01  15.075  < 2e-16 ***
## b   1.561e+02  9.184e+00  17.001  < 2e-16 ***
## c   2.015e+02  2.745e+01   7.339 2.28e-13 ***
## d   2.088e+00  8.854e-02  23.577  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6385 on 12424 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (40 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   1258     341.03                          
## 2   1257     340.57  1 0.45741  1.6882 0.1941
##   model      AIC
## 1     1 14066.84
## 2     2 14067.14
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)
## ge 3.821e-02  3.664e-01   0.104    0.917
## a  1.252e+01  1.911e+01   0.655    0.512
## b  8.328e+02  2.810e+03   0.296    0.767
## c  5.000e+03  3.947e+04   0.127    0.899
## d  3.188e+00  3.021e+00   1.055    0.292
## 
## Residual standard error: 0.5207 on 1258 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96304, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -11.433, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Error in nls(f_ln_1, data = G_242, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = G_242, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
## Error in as.formula(formula) : object 'f_ln_3' not found
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_242.", Mod.Sel1, sep = "")) : 
##   object 'nls_242.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

251 - Prairie Parkland (Temperate)

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1791     389.13                           
## 2   1790     389.12  1 0.014975  0.0689  0.793
##   model      AIC
## 1     1 18723.44
## 2     2 18725.38
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.1803     0.2334  -0.772     0.44    
## a   26.7896     4.8189   5.559 3.12e-08 ***
## b  101.6305     8.4399  12.042  < 2e-16 ***
## c  104.5991     8.4270  12.412  < 2e-16 ***
## d    1.1194     0.1084  10.324  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4661 on 1791 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9698, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -17.299, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1    656     205.66                              
## 2    655     205.66  1 -1.9804e-10       0      1
##   model      AIC
## 1     1 6693.871
## 2     2 6695.871
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.7402     0.3111  -2.380 0.017618 *  
## a   17.9145     4.7506   3.771 0.000177 ***
## b   86.3366     9.7381   8.866  < 2e-16 ***
## c   67.8705     9.9633   6.812 2.18e-11 ***
## d    1.2644     0.1798   7.031 5.17e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5599 on 656 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94097, p-value = 1.548e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.1924, p-value = 2.56e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

## Error in nls(f_ln_1, data = G_261, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = G_261, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
## Error in as.formula(formula) : object 'f_ln_3' not found
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_261$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_261.", Mod.Sel1, sep = "")) : 
##   object 'nls_261.' not found

summary

  • simple model: does not fit

  • phi model: does not fit

  • phi-alpha model: does not fit

  • unable to fit model (only 64 observations)

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

262 - California Dry Steppe

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in as.formula(formula) : object 'f_ln_3' not found
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_262$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_262.", Mod.Sel1, sep = "")) : 
##   object 'nls_262.' not found

summary

  • simple model: does not fit

  • phi model: does not fit

  • phi-alpha model: does not fit

  • unable to fit model (0 observations)

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1    149     26.638                              
## 2    148     26.638  1 -3.6088e-11       0      1
##   model      AIC
## 1     1 1935.134
## 2     2 1937.134
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge    1.224      2.254   0.543   0.5879  
## a     0.000     69.109   0.000   1.0000  
## b  1000.000    913.184   1.095   0.2753  
## c  1898.226   4726.971   0.402   0.6886  
## d     2.777      1.518   1.830   0.0693 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4228 on 149 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97748, p-value = 0.0126
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.2016, p-value = 0.0277
## alternative hypothesis: two.sided

predict and plot

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Error in nls(f_ln_1, data = G_313, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = G_313, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
## Error in as.formula(formula) : object 'f_ln_3' not found
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_313.", Mod.Sel1, sep = "")) : 
##   object 'nls_313.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model
  • not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df     Sum Sq F value Pr(>F)
## 1    298     169.14                             
## 2    297     169.14  1 9.3792e-13       0      1
##   model      AIC
## 1     1 3100.582
## 2     2 3102.582
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge   0.4889     1.4827   0.330   0.7418  
## a    0.0000    19.2900   0.000   1.0000  
## b   52.4290    27.5134   1.906   0.0577 .
## c  119.8342    66.7961   1.794   0.0738 .
## d    2.1713     1.2242   1.774   0.0771 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7534 on 298 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.8809, p-value = 1.318e-14
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.2814, p-value = 3.356e-10
## alternative hypothesis: two.sided

predict and plot

plotting 2

* Cannot fit model

332 - Great Plains Steppe

model selection 1

## Error in nls(f_ln_1, data = G_332, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_2, data = G_332, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in as.formula(formula) : object 'f_ln_3' not found
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_332$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_332.", Mod.Sel1, sep = "")) : 
##   object 'nls_332.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model not fitted because only 62 observations

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

342 - Intermountain Semi-Desert

model selection 1

## Error in nls(f_ln_1, data = G_342, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = G_342, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
## Error in as.formula(formula) : object 'f_ln_3' not found
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_342$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_342.", Mod.Sel1, sep = "")) : 
##   object 'nls_342.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6721     1270.3                                
## 2   6720     1264.3  1 6.0317   32.06 1.557e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 71115.80
## 2     2 71085.79
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  3.971e-01  1.651e-01   2.405 0.016185 *  
## phi 3.406e-02  6.266e-03   5.435 5.67e-08 ***
## a   9.561e+00  2.760e+00   3.464 0.000536 ***
## b   1.717e+02  1.677e+01  10.241  < 2e-16 ***
## c   2.925e+02  5.966e+01   4.902 9.69e-07 ***
## d   1.911e+00  1.504e-01  12.710  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4337 on 6720 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df     Sum Sq F value Pr(>F)
## 1   8027     1280.2                             
## 2   8026     1280.2  1 2.6262e-10       0      1
##   model      AIC
## 1     1 88546.92
## 2     2 88548.92
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge   0.7642     0.1214   6.294 3.27e-10 ***
## a   31.0606     2.0118  15.439  < 2e-16 ***
## b  118.2933     3.7643  31.425  < 2e-16 ***
## c  106.0278     3.6034  29.424  < 2e-16 ***
## d    1.2855     0.0479  26.839  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3994 on 8027 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

predict and plot

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Error in nls(f_ln_1, data = G_M223, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_2, data = G_M223, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in as.formula(formula) : object 'f_ln_3' not found
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M223$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_M223.", Mod.Sel1, sep = "")) : 
##   object 'nls_M223.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M231 - Ouachita Mixed Forest

model selection 1

## Error in nls(f_ln_1, data = G_M231, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_2, data = G_M231, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in as.formula(formula) : object 'f_ln_3' not found
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M231$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_M231.", Mod.Sel1, sep = "")) : 
##   object 'nls_M231.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M242 - Cascade Mixed Forest

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df     Sum Sq F value Pr(>F)
## 1   3172     1918.7                             
## 2   3171     1918.7  1 4.3201e-12       0      1
##   model      AIC
## 1     1 41988.35
## 2     2 41990.35
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge   0.2910     0.6403   0.454 0.649541    
## a    0.0000     7.1556   0.000 1.000000    
## b  485.8141    88.9523   5.462 5.08e-08 ***
## c  828.2527   233.3203   3.550 0.000391 ***
## d    2.3429     0.2025  11.569  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7777 on 3172 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94202, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -20.536, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1952    1001.42                                
## 2   1951     925.67  1 75.745  159.64 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24765.07
## 2     2 24613.15
## 3     3       NA

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90919, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.0536, p-value = 0.002261
## alternative hypothesis: two.sided

predict and plot

plotting 2

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    356     110.33                            
## 2    355     109.15  1 1.1717  3.8108 0.05171 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3771.802
## 2     2 3769.947
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -1.71927    0.37661  -4.565 6.89e-06 ***
## phi   0.05390    0.02373   2.272 0.023713 *  
## a    48.59296   14.49239   3.353 0.000886 ***
## b   168.46758   35.84542   4.700 3.73e-06 ***
## c   146.48390   16.95487   8.640  < 2e-16 ***
## d     0.72919    0.12688   5.747 1.96e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5545 on 355 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93581, p-value = 2.293e-11
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.63435, p-value = 0.5259
## alternative hypothesis: two.sided

predict and plot

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   1691     583.39                          
## 2   1690     583.09  1 0.30785  0.8923  0.345
##   model      AIC
## 1     1 17699.64
## 2     2 17700.75
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.8186     0.3694  -2.216   0.0268 *  
## a   25.5229     3.9126   6.523 9.06e-11 ***
## b  117.4741    15.8948   7.391 2.28e-13 ***
## c  225.0966    28.7043   7.842 7.80e-15 ***
## d    1.3310     0.1247  10.676  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5874 on 1691 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (15 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92395, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.869, p-value = 1.122e-06
## alternative hypothesis: two.sided

predict and plot

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)   
## 1   2641     1154.9                             
## 2   2640     1151.5  1 3.4132  7.8251 0.00519 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 28864.48
## 2     2 28858.65
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.47444    0.70178   0.676  0.49906    
## phi   0.04074    0.01395   2.919  0.00354 ** 
## a    20.29162    3.68757   5.503 4.10e-08 ***
## b   100.10614   17.56772   5.698 1.34e-08 ***
## c   222.59104   22.92826   9.708  < 2e-16 ***
## d     1.36913    0.10494  13.047  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6604 on 2640 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89566, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.3736, p-value = 1.222e-05
## alternative hypothesis: two.sided

predict and plot

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   1665     654.15                          
## 2   1664     653.64  1 0.51096  1.3008 0.2542
##   model      AIC
## 1     1 18742.43
## 2     2 18743.13
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   2.00819    1.73755   1.156 0.247943    
## a   14.15851    4.36299   3.245 0.001197 ** 
## b   88.92272   26.87216   3.309 0.000956 ***
## c  134.44260    6.30013  21.340  < 2e-16 ***
## d    1.04023    0.05219  19.931  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6268 on 1665 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (5 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93299, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.5759, p-value = 4.742e-06
## alternative hypothesis: two.sided

predict and plot

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    356     147.67                            
## 2    355     146.35  1 1.3214  3.2053 0.07425 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3622.910
## 2     2 3621.665
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -1.43327    0.40123  -3.572 0.000403 ***
## phi   0.05965    0.03391   1.759 0.079456 .  
## a     4.23809   17.78884   0.238 0.811829    
## b    94.02653   28.41884   3.309 0.001034 ** 
## c   172.96057   97.90646   1.767 0.078156 .  
## d     1.81753    0.72623   2.503 0.012774 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6421 on 355 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93172, p-value = 8.478e-12
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.0543, p-value = 1.41e-09
## alternative hypothesis: two.sided

predict and plot

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df     Sum Sq F value Pr(>F)
## 1    207     64.472                             
## 2    206     64.472  1 1.1369e-12       0      1
##   model      AIC
## 1     1 2088.502
## 2     2 2090.502
## 3     3       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -1.5120     0.5190  -2.913  0.00397 ** 
## a   24.5523     6.2269   3.943  0.00011 ***
## b  100.9276    22.6252   4.461 1.34e-05 ***
## c  145.9339    14.5564  10.025  < 2e-16 ***
## d    0.8985     0.1519   5.917 1.34e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5581 on 207 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92868, p-value = 1.246e-08
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.78699, p-value = 0.4313
## alternative hypothesis: two.sided

predict and plot

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest NA
212 Laurentian Mixed Forest 2
221 Eastern Broadleaf Forest 1
222 Midwest Broadleaf Forest 2
223 Central Interior Broadleaf Forest 1
231 Southeastern Mixed Forest 1
232 Outer Coastal Plain Mixed Forest 2
234 Lower Mississippi Riverine Forest 1
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 1
255 Prairie Parkland (Subtropical) 1
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest 1
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe 1
332 Great Plains Steppe NA
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 1
M223 Ozark Broadleaf Forest Meadow NA
M231 Ouachita Mixed Forest NA
M242 Cascade Mixed Forest 1
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 2
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 1
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 1
M334 Black Hills Coniferous Forest 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow 1

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.2.5 ge.97.5 phi phi.2.5 phi.97.5 alpha alpha.2.5 alpha.97.5 a a.2.5 a.97.5 b b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 6806 2847 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
212 Laurentian Mixed Forest east 18775 8891 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
221 Eastern Broadleaf Forest east 7170 3490 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
222 Midwest Broadleaf Forest east 4877 2401 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
223 Central Interior Broadleaf Forest east 8783 3725 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
231 Southeastern Mixed Forest east 12347 5691 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
232 Outer Coastal Plain Mixed Forest east 12470 6101 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
234 Lower Mississippi Riverine Forest east 1265 714 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
242 Pacific Lowland Mixed Forest pacific 81 81 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1797 809 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
255 Prairie Parkland (Subtropical) pacific 663 293 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
261 California Coastal Chaparral Forest and Shrub pacific 24 24 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 155 155 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 215 215 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 304 240 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 195 106 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
341 Intermountain Semi-Desert and Desert interior west 62 62 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 121 120 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 93 61 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6729 2989 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8034 3700 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M223 Ozark Broadleaf Forest Meadow east 883 343 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M231 Ouachita Mixed Forest east 988 481 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M242 Cascade Mixed Forest pacific 3179 3176 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 1963 1963 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 19 19 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 362 362 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 1711 1711 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 2649 2648 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 1675 1675 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest interior west 362 170 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 213 213 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

map #2

plot phi (effect of DeltaPDSI)

plot alpha (biomass compensation effect)

plot a coefficient

## Warning: Removed 36 rows containing missing values (geom_point).

plot b coefficient

## Warning: Removed 36 rows containing missing values (geom_point).

plot c coefficient

## Warning: Removed 36 rows containing missing values (geom_point).

plot d coefficient

## Warning: Removed 36 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass enhancement factor in % 2000-2021)

##          region weighted.ge
## 1     entire US           0
## 2       pacific           0
## 3          east           0
## 4 interior west           0

phi (effect of DeltaPDSI)

##          region weighted.phi
## 1     entire US            0
## 2       pacific            0
## 3          east            0
## 4 interior west            0

alpha (biomass compensation effect)

##          region weighted.alpha
## 1     entire US              0
## 2       pacific              0
## 3          east              0
## 4 interior west              0

Calculations - weighted averages subsetted to 15 ecoprovinces

  • 211, 212, 221, 223, 231, 232, 234, 251, M211, M221, M223, M231, M242, M261, M332

ge

##          region weighted.ge
## 1     entire US           0
## 2       pacific           0
## 3          east           0
## 4 interior west           0

phi

##          region weighted.phi
## 1     entire US            0
## 2       pacific            0
## 3          east            0
## 4 interior west            0

alpha

##          region weighted.alpha
## 1     entire US              0
## 2       pacific              0
## 3          east              0
## 4 interior west              0